7K^2+34K-5=0

Solution for 7K^2+34K-5=0 equation:

Simplifying
7K2 + 34K + -5 = 0

Reorder the terms:
-5 + 34K + 7K2 = 0

Solving
-5 + 34K + 7K2 = 0

Solving for variable 'K'.

Factor a trinomial.
(-5 + -1K)(1 + -7K) = 0

Subproblem 1
Set the factor '(-5 + -1K)' equal to zero and attempt to solve:

Simplifying
-5 + -1K = 0

Solving
-5 + -1K = 0

Move all terms containing K to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1K = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1K = 0 + 5
-1K = 0 + 5

Combine like terms: 0 + 5 = 5
-1K = 5

Divide each side by '-1'.
K = -5

Simplifying
K = -5
Subproblem 2
Set the factor '(1 + -7K)' equal to zero and attempt to solve:

Simplifying
1 + -7K = 0

Solving
1 + -7K = 0

Move all terms containing K to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -7K = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7K = 0 + -1
-7K = 0 + -1

Combine like terms: 0 + -1 = -1
-7K = -1

Divide each side by '-7'.
K = 0.1428571429

Simplifying
K = 0.1428571429
Solution
K = {-5, 0.1428571429}